CHE 499 (Spring 04) __________________ LAST NAME, FIRST Problem set #41. (p. 7.261) During cardiopulmonary bypass, in open-heart surgery, the blood is cooled by an external heatexchanger to lower the body temperature. This loweringof the body temperature (called whole-bodyhypothermia) reduces metabolic demand and protectsthe vital organs during the operation. The heatexchanger is part of the extra-corporeal circulationcircuit where special pumps (e.g., roller pumps, whichuse compression of elastic tubes to move the liquid) areused to protect the blood cells from mechanicaldamage. A shell and tube heat exchanger (with one shellpass) is used to cool (and later heat) the bloodstream atTh,i, using a water stream, as shown in Figure 1, to thehypothermic temperature Th,o. (a) Determine the bloodstream exit temperature Th,o.(b) Determine the heat transfer rate in W.Th,i = 37oC, Tc,i = 15oC, (Mf /f )h = 250 ml/min, (Mf/f )c = 200 ml/min, UA = 20 W/C. Use Cp,f = 4182 J/kgK and f = 997.7 kg/m3 for both blood and water.Figure 1. Blood heat exchanger.2. (p. 14.222) Pulverized coal, which may be approximated as carbon spheres of radius R = 1mm, is burned in a pure oxygen atmosphere at 1450oK and 1 atm. Oxygen is transferred tothe particle surface by diffusion, where it is consumed in the reaction C + O2  CO2Assuming the surface reaction rate to be infinite and neglecting change in R, determine thesteady state O2 molar consumption rate in kmol/s. At 1450oK, the binary diffusion coefficientfor O2 and CO2 is 1.7110-4 m2/s. Plot the radial distribution of the O2 and CO2 molefractions from r = R to r = 4R.3. A ice cube Ts = 0oC is brought in contact with human skin having Cp = 3.7×106 J/m3C, k =0.293 W/mC, and T(t = 0) = 37oC for a total elapsed time of t = 300 s. The surface area of1 Kaviany, Principles of Heat Transfer, Wiley, 2002, p. 3502 Incropera, Fundamentals of Heat and Mass Transfer, Wiley, 2002heat transfer is 100 cm2. Use the solution for transient conduction through a semi-infinite slabwith prescribed surface temperature to determine the amount (J) of heat transfer from theskin to the ice during this elapsed time.4. Use nonlinear regression to fit a saturation-growth-rate equation, y = axbx, to the datax5 10 15 20 25 30 35 40 45 50y16 25 32 33 38 36 39 40 42 42Use the first guest a = 50, b = 10(a) Use the Matlab given in Table A-1 to print out the values of [Zj]T[Zj], {D}, [Zj]T{D}, and{A} for two iterations.(b) Use the Matlab given in Table A-2 to calculate the final values for a and b. Calculate thestandard error and the correlation coefficient.(c) Use Matlab function fminsearch to calculate the final values for a and b.(d) Use Excel Solver to calculate the final values for a and b.5. Fit the function T(t; , h) = (1  eht) to the data.t0.25 0.75 1.25 1.75 2.25T0.28 0.75 0.68 0.74 0.79Use initial guesses of h = 1 and  = 1 for the parameters. Using hand calculation to verify the following matrices and vectors:(a) [Zj]T[Zj] = 4404.09489.09489.03194.2(b) {D} = 1046.00862.00335.00424.00588.0(c) [Zj]T{D} = 0365.01533.0 (d) {A} =